file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/Int/Order/Basic.lean | Int.sign_mul_abs | [
{
"state_after": "no goals",
"state_before": "a : ℤ\n⊢ sign a * abs a = a",
"tactic": "rw [abs_eq_natAbs, sign_mul_natAbs a]"
}
] | [
75,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.of_mulEquivOfMulEquiv_apply | [] | [
1595,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1592,
1
] |
Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | HasStrictDerivAt.exp | [] | [
225,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_iInter_subset | [] | [
276,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/Algebra/Order/UpperLower.lean | LowerSet.coe_mul | [] | [
218,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Topology/Category/TopCat/Opens.lean | TopologicalSpace.Opens.adjunction_counit_map_functor | [
{
"state_after": "X : TopCat\nU : Opens ↑X\nV : Opens { x // x ∈ U }\n⊢ (IsOpenMap.functor (_ : IsOpenMap ((forget TopCat).map (inclusion U)))).obj\n ((map (inclusion U)).obj ((IsOpenMap.functor (_ : IsOpenMap ((forget TopCat).map (inclusion U)))).obj V)) =\n (IsOpenMap.functor (_ : IsOpenMap ((forget T... | [
409,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
] |
Mathlib/Data/Finset/Prod.lean | Finset.offDiag_union | [
{
"state_after": "α : Type u_1\nβ : Type ?u.123926\nγ : Type ?u.123929\ninst✝ : DecidableEq α\ns t : Finset α\nx : α × α\nh : _root_.Disjoint s t\n⊢ Set.offDiag (↑s ∪ ↑t) = Set.offDiag ↑s ∪ Set.offDiag ↑t ∪ ↑s ×ˢ ↑t ∪ ↑t ×ˢ ↑s",
"state_before": "α : Type u_1\nβ : Type ?u.123926\nγ : Type ?u.123929\ninst✝ : ... | [
403,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.card_Ioo_eq_card_Icc_sub_two | [] | [
239,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Std/Data/List/Lemmas.lean | List.get?_eq_get | [] | [
507,
45
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
505,
1
] |
Mathlib/Topology/ExtendFrom.lean | continuous_extendFrom | [
{
"state_after": "X : Type u_2\nY : Type u_1\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : RegularSpace Y\nf : X → Y\nA : Set X\nhA : Dense A\nhf : ∀ (x : X), ∃ y, Tendsto f (𝓝[A] x) (𝓝 y)\n⊢ ContinuousOn (extendFrom A f) univ",
"state_before": "X : Type u_2\nY : Type u_1\ninst✝² : To... | [
92,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | lt_mul_left | [
{
"state_after": "case h.e'_3\nα : Type u\nβ : Type ?u.61774\ninst✝ : StrictOrderedSemiring α\na b c d : α\nhn : 0 < a\nhm : 1 < b\n⊢ a = 1 * a",
"state_before": "α : Type u\nβ : Type ?u.61774\ninst✝ : StrictOrderedSemiring α\na b c d : α\nhn : 0 < a\nhm : 1 < b\n⊢ a < b * a",
"tactic": "convert mul_lt_... | [
565,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
563,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | SequentiallyComplete.setSeq_sub_aux | [] | [
665,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
664,
1
] |
Mathlib/Order/Heyting/Hom.lean | CoheytingHom.toFun_eq_coe | [] | [
389,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/Topology/ContinuousOn.lean | ContinuousWithinAt.congr_of_eventuallyEq | [] | [
963,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
960,
1
] |
Mathlib/GroupTheory/QuotientGroup.lean | QuotientGroup.homQuotientZPowOfHom_comp_of_rightInverse | [] | [
525,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/Analysis/Calculus/IteratedDeriv.lean | iteratedDeriv_succ | [
{
"state_after": "case h\n𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type ?u.134653\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nn : ℕ\nf : 𝕜 → F\ns : Set 𝕜\nx✝ x : 𝕜\n⊢ iteratedDeriv (n + 1) f x = deriv (iterat... | [
293,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/Data/List/Sigma.lean | List.kunion_kerase | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : α → Type v\nl✝ l₁ l₂ : List (Sigma β)\ninst✝ : DecidableEq α\na : α\ns : Sigma β\ntail✝ : List (Sigma β)\nl : List (Sigma β)\n⊢ kunion (kerase a (s :: tail✝)) (kerase a l) = kerase a (kunion (s :: tail✝) l)",
"tactic": "by_cases h : a = s.1 <... | [
713,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
710,
1
] |
Mathlib/Data/PFunctor/Multivariate/Basic.lean | MvPFunctor.id_map | [] | [
69,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/CategoryTheory/Category/Basic.lean | CategoryTheory.cancel_mono | [] | [
292,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.op_norm_nonneg | [] | [
332,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/Analysis/SpecialFunctions/CompareExp.lean | Complex.IsExpCmpFilter.tendsto_abs_re | [] | [
103,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Topology/MetricSpace/Baire.lean | mem_residual | [
{
"state_after": "case mp\nα : Type u_1\nβ : Type ?u.14520\nγ : Type ?u.14523\nι : Type ?u.14526\ninst✝¹ : TopologicalSpace α\ninst✝ : BaireSpace α\ns : Set α\n⊢ s ∈ residual α → ∃ t x, IsGδ t ∧ Dense t\n\ncase mpr\nα : Type u_1\nβ : Type ?u.14520\nγ : Type ?u.14523\nι : Type ?u.14526\ninst✝¹ : TopologicalSpace... | [
239,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_eq_one' | [] | [
138,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Embedding.refl_apply | [] | [
702,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
701,
1
] |
Mathlib/RingTheory/Polynomial/Bernstein.lean | bernsteinPolynomial.eval_at_0 | [
{
"state_after": "R : Type u_1\ninst✝ : CommRing R\nn ν : ℕ\n⊢ Polynomial.eval 0 (↑(choose n ν) * X ^ ν * (1 - X) ^ (n - ν)) = if ν = 0 then 1 else 0",
"state_before": "R : Type u_1\ninst✝ : CommRing R\nn ν : ℕ\n⊢ Polynomial.eval 0 (bernsteinPolynomial R n ν) = if ν = 0 then 1 else 0",
"tactic": "rw [be... | [
96,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/FieldTheory/Minpoly/Field.lean | minpoly.degree_le_of_ne_zero | [
{
"state_after": "no goals",
"state_before": "A : Type u_1\nB : Type u_2\ninst✝² : Field A\ninst✝¹ : Ring B\ninst✝ : Algebra A B\nx : B\np : A[X]\npnz : p ≠ 0\nhp : ↑(Polynomial.aeval x) p = 0\n⊢ ↑(Polynomial.aeval x) (p * ↑C (leadingCoeff p)⁻¹) = 0",
"tactic": "simp [hp]"
}
] | [
45,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/Data/Real/ENNReal.lean | Set.OrdConnected.image_ennreal_ofReal | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.872272\nβ : Type ?u.872275\ns : Set ℝ\nt : Set ℝ≥0\nu : Set ℝ≥0∞\nh : OrdConnected s\n⊢ OrdConnected (ENNReal.ofReal '' s)",
"tactic": "simpa only [image_image] using h.image_real_toNNReal.image_coe_nnreal_ennreal"
}
] | [
2523,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2522,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | dist_lt_coe | [] | [
361,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.vsub_inter_subset | [] | [
697,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.pred_lt_iff_of_not_isMin | [] | [
637,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.le_add_right | [] | [
996,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
996,
11
] |
Mathlib/Topology/Sets/Closeds.lean | TopologicalSpace.Closeds.iInf_mk | [] | [
180,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | HasFTaylorSeriesUpTo.hasFTaylorSeriesUpToOn | [] | [
1251,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1249,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.toDeleteEdges_nil | [] | [
1787,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1786,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | measurable_measure_prod_mk_left | [
{
"state_after": "α : Type u_2\nα' : Type ?u.1887086\nβ : Type u_1\nβ' : Type ?u.1887092\nγ : Type ?u.1887095\nE : Type ?u.1887098\ninst✝⁶ : MeasurableSpace α\ninst✝⁵ : MeasurableSpace α'\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace β'\ninst✝² : MeasurableSpace γ\nμ μ' : MeasureTheory.Measure α\nν ν' :... | [
189,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Logic/Encodable/Basic.lean | Encodable.encode_inj | [] | [
73,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.iSupLift_comp_inclusion | [
{
"state_after": "case H\nR : Type u\nA : Type v\nB : Type w\ninst✝⁵ : CommSemiring R\ninst✝⁴ : Semiring A\ninst✝³ : Algebra R A\ninst✝² : Semiring B\ninst✝¹ : Algebra R B\nS : Subalgebra R A\nι : Type u_1\ninst✝ : Nonempty ι\nK : ι → Subalgebra R A\ndir : Directed (fun x x_1 => x ≤ x_1) K\nf : (i : ι) → { x //... | [
1219,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1218,
1
] |
Mathlib/Data/Set/Image.lean | Set.image_subset_range | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.70476\nι : Sort ?u.70479\nι' : Sort ?u.70482\nf✝ : ι → α\ns✝ t : Set α\nf : α → β\ns : Set α\n⊢ f '' s ⊆ f '' univ",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.70476\nι : Sort ?u.70479\nι' : Sort ?u.70482\nf✝ : ι → α\ns✝ t : Set α\nf : ... | [
700,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
699,
1
] |
Mathlib/Topology/Connected.lean | isTotallyDisconnected_of_image | [] | [
1342,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1337,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_inl | [] | [
987,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
986,
1
] |
Mathlib/Data/Nat/Parity.lean | Nat.even_sub | [
{
"state_after": "m n : ℕ\nh : n ≤ m\n⊢ Even (m - n) ↔ ((Even (m - n) ↔ Even n) ↔ Even n)",
"state_before": "m n : ℕ\nh : n ≤ m\n⊢ Even (m - n) ↔ (Even m ↔ Even n)",
"tactic": "conv_rhs => rw [← tsub_add_cancel_of_le h, even_add]"
},
{
"state_after": "no goals",
"state_before": "m n : ℕ\nh :... | [
143,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/NumberTheory/Padics/Hensel.lean | bound' | [
{
"state_after": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nF : Polynomial ℤ_[p]\na : ℤ_[p]\nhnorm : ‖Polynomial.eval a F‖ < ‖Polynomial.eval a (↑Polynomial.derivative F)‖ ^ 2\nhnsol : Polynomial.eval a F ≠ 0\n⊢ Tendsto (fun n => ‖Polynomial.eval a (↑Polynomial.derivative F)‖ * T_gen p F a ^ 2 ^ n) atTop\n (𝓝 (‖Po... | [
354,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
9
] |
Std/Data/List/Basic.lean | List.enumFrom_eq_enumFromTR | [
{
"state_after": "case h.h.h\nα : Type u_1\nn : Nat\nl : List α\n⊢ enumFrom n l = enumFromTR n l",
"state_before": "⊢ @enumFrom = @enumFromTR",
"tactic": "funext α n l"
},
{
"state_after": "case h.h.h\nα : Type u_1\nn : Nat\nl : List α\n⊢ enumFrom n l =\n (Array.foldr (fun a x => (x.fst - 1, ... | [
206,
44
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
199,
10
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.zeroLocus_mul | [] | [
370,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.submoduleMap_apply | [] | [
1897,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1896,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Monad.lean | Pmf.pure_bind | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.56970\np : Pmf α\nf✝ : α → Pmf β\ng : β → Pmf γ\na : α\nf : α → Pmf β\nthis : ∀ (b : β) (a' : α), (if a' = a then ↑(f a') b else 0) = if a' = a then ↑(f a) b else 0\n⊢ bind (pure a) f = f a",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.5... | [
138,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | linearIndependent_pair | [] | [
1227,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1224,
1
] |
Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.adjugate_smul | [
{
"state_after": "m : Type u\nn : Type v\nα : Type w\ninst✝⁴ : DecidableEq n\ninst✝³ : Fintype n\ninst✝² : DecidableEq m\ninst✝¹ : Fintype m\ninst✝ : CommRing α\nr : α\nA : Matrix n n α\n⊢ (↑of fun i => ↑(r ^ (Fintype.card n - 1) • cramer Aᵀ) (Pi.single i 1)) =\n r ^ (Fintype.card n - 1) • ↑of fun i => ↑(cra... | [
308,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.cthickening_singleton | [
{
"state_after": "case h\nι : Sort ?u.105056\nα✝ : Type u\nβ : Type v\ninst✝¹ : PseudoEMetricSpace α✝\nδ✝ ε : ℝ\ns t : Set α✝\nx✝ : α✝\nα : Type u_1\ninst✝ : PseudoMetricSpace α\nx : α\nδ : ℝ\nhδ : 0 ≤ δ\ny : α\n⊢ y ∈ cthickening δ {x} ↔ y ∈ closedBall x δ",
"state_before": "ι : Sort ?u.105056\nα✝ : Type u\... | [
1086,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1083,
1
] |
Mathlib/Order/Filter/IndicatorFunction.lean | Monotone.tendsto_indicator | [
{
"state_after": "case pos\nα : Type u_3\nβ : Type u_2\nM : Type ?u.3017\nE : Type ?u.3020\nι : Type u_1\ninst✝¹ : Preorder ι\ninst✝ : Zero β\ns : ι → Set α\nhs : Monotone s\nf : α → β\na : α\nh : ∃ i, a ∈ s i\n⊢ Tendsto (fun i => indicator (s i) f a) atTop (pure (indicator (⋃ (i : ι), s i) f a))\n\ncase neg\nα... | [
73,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.rpow_lt_rpow | [] | [
149,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/MeasureTheory/Function/UniformIntegrable.lean | MeasureTheory.UniformIntegrable.spec | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nι : Type u_3\nm : MeasurableSpace α\nμ : Measure α\ninst✝ : NormedAddCommGroup β\np : ℝ≥0∞\nf : ι → α → β\nhp : p ≠ 0\nhp' : p ≠ ⊤\nhfu : UniformIntegrable f p μ\nε : ℝ\nhε : 0 < ε\ng : ι → α → β := fun i => Exists.choose (_ : AEStronglyMeasurable (f i) μ)\n⊢ ∃ C, ∀... | [
908,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
895,
1
] |
Mathlib/GroupTheory/GroupAction/Basic.lean | MulAction.orbitRel.Quotient.orbit_eq_orbit_out | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : Group α\ninst✝ : MulAction α β\nx : Quotient α β\nφ : Quotient α β → β\nhφ : Function.RightInverse φ Quotient.mk'\n⊢ orbit x = MulAction.orbit α (φ x)",
"tactic": "conv_lhs => rw [← hφ x]"
}
] | [
377,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Algebra/ContinuedFractions/ConvergentsEquiv.lean | GeneralizedContinuedFraction.squashGCF_eq_self_of_terminated | [
{
"state_after": "case zero\nK : Type u_1\ng : GeneralizedContinuedFraction K\ns : Stream'.Seq (Pair K)\ninst✝ : DivisionRing K\nterminated_at_n : TerminatedAt g Nat.zero\n⊢ squashGCF g Nat.zero = g\n\ncase succ\nK : Type u_1\ng : GeneralizedContinuedFraction K\ns : Stream'.Seq (Pair K)\ninst✝ : DivisionRing K\... | [
218,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/LinearAlgebra/Quotient.lean | Submodule.mkQ_map_self | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nM : Type u_1\nr : R\nx y : M\ninst✝⁵ : Ring R\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\np p' : Submodule R M\nR₂ : Type ?u.231258\nM₂ : Type ?u.231261\ninst✝² : Ring R₂\ninst✝¹ : AddCommGroup M₂\ninst✝ : Module R₂ M₂\nτ₁₂ : R →+* R₂\n⊢ map (mk... | [
390,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
Mathlib/MeasureTheory/Group/Action.lean | MeasureTheory.measure_pos_iff_nonempty_of_smulInvariant | [] | [
251,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haar.prehaar_nonneg | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : TopologicalSpace G\nK₀ : PositiveCompacts G\nU : Set G\nK : Compacts G\n⊢ 0 ≤ prehaar (↑K₀) U K",
"tactic": "apply div_nonneg <;> norm_cast <;> apply zero_le"
}
] | [
132,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_prod | [] | [
1133,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1131,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.singletonSubgraph_eq_induce | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.261642\nV : Type u\nW : Type v\nG : SimpleGraph V\nG' G'' : Subgraph G\ns s' : Set V\nv : V\n⊢ SimpleGraph.singletonSubgraph G v = induce ⊤ {v}",
"tactic": "ext <;> simp (config := { contextual := true }) [-Set.bot_eq_empty, Prop.bot_eq_false]"
... | [
1183,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1182,
1
] |
Mathlib/LinearAlgebra/TensorAlgebra/Basic.lean | TensorAlgebra.ι_ne_one | [
{
"state_after": "R : Type u_1\ninst✝³ : CommSemiring R\nM : Type u_2\ninst✝² : AddCommMonoid M\ninst✝¹ : Module R M\ninst✝ : Nontrivial R\nx : M\n⊢ ¬(x = 0 ∧ 1 = 0)",
"state_before": "R : Type u_1\ninst✝³ : CommSemiring R\nM : Type u_2\ninst✝² : AddCommMonoid M\ninst✝¹ : Module R M\ninst✝ : Nontrivial R\nx... | [
280,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Data/Complex/Module.lean | Complex.smul_re | [] | [
64,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Topology/Connected.lean | isClosed_connectedComponent | [] | [
706,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
1
] |
Mathlib/Data/Nat/Factorial/Basic.lean | Nat.factorial_two | [] | [
62,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Algebra/Module/Submodule/Lattice.lean | Submodule.sInf_le' | [] | [
203,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
9
] |
Mathlib/Order/Compare.lean | Ordering.orElse_eq_lt | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.10115\nβ : Type ?u.10118\no₁ o₂ : Ordering\n⊢ orElse o₁ o₂ = lt ↔ o₁ = lt ∨ o₁ = eq ∧ o₂ = lt",
"tactic": "cases o₁ <;> cases o₂ <;> exact by decide"
},
{
"state_after": "no goals",
"state_before": "α : Type ?u.10115\nβ : Type ?u.1011... | [
149,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/MeasureTheory/Decomposition/SignedHahn.lean | MeasureTheory.SignedMeasure.existsNatOneDivLTMeasure_of_not_negative | [] | [
106,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
9
] |
Mathlib/ModelTheory/Skolem.lean | FirstOrder.Language.exists_small_elementarySubstructure | [] | [
125,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/ModelTheory/ElementaryMaps.lean | FirstOrder.Language.ElementaryEmbedding.map_rel | [] | [
153,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Computability/DFA.lean | DFA.evalFrom_singleton | [] | [
63,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/CategoryTheory/Category/Preorder.lean | CategoryTheory.leOfHom_homOfLE | [] | [
100,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/RingTheory/Localization/Away/Basic.lean | selfZpow_coe_nat | [] | [
221,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/CategoryTheory/Preadditive/ProjectiveResolution.lean | CategoryTheory.ProjectiveResolution.complex_d_comp_π_f_zero | [] | [
125,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Data/Polynomial/Laurent.lean | LaurentPolynomial.isLocalization | [
{
"state_after": "case mk\nR : Type u_1\ninst✝ : CommSemiring R\nt : R[X]\nht : t ∈ Submonoid.closure {X}\n⊢ IsUnit (↑(algebraMap R[X] R[T;T⁻¹]) ↑{ val := t, property := ht })",
"state_before": "R : Type u_1\ninst✝ : CommSemiring R\nt : { x // x ∈ Submonoid.closure {X} }\n⊢ IsUnit (↑(algebraMap R[X] R[T;T⁻¹... | [
611,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.isBoundedUnder_le_inv | [] | [
266,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Data/Int/ModEq.lean | Int.ModEq.mul | [] | [
208,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
11
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.graph_map_fst_eq_domain | [
{
"state_after": "case h\nR : Type u_1\ninst✝⁶ : Ring R\nE : Type u_2\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module R E\nF : Type u_3\ninst✝³ : AddCommGroup F\ninst✝² : Module R F\nG : Type ?u.484814\ninst✝¹ : AddCommGroup G\ninst✝ : Module R G\nf : E →ₗ.[R] F\nx : E\n⊢ x ∈ Submodule.map (LinearMap.fst R E F) (grap... | [
749,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
740,
1
] |
Std/Data/Int/Lemmas.lean | Int.le_sub_left_of_add_le | [
{
"state_after": "a b c : Int\nh✝ : a + b ≤ c\nh : a + b + -a ≤ c + -a\n⊢ b ≤ c - a",
"state_before": "a b c : Int\nh : a + b ≤ c\n⊢ b ≤ c - a",
"tactic": "have h := Int.add_le_add_right h (-a)"
},
{
"state_after": "no goals",
"state_before": "a b c : Int\nh✝ : a + b ≤ c\nh : a + b + -a ≤ c ... | [
964,
56
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
962,
11
] |
Mathlib/Analysis/MeanInequalities.lean | Real.geom_mean_eq_arith_mean_weighted_of_constant | [
{
"state_after": "no goals",
"state_before": "ι : Type u\ns : Finset ι\nw z : ι → ℝ\nx : ℝ\nhw : ∀ (i : ι), i ∈ s → 0 ≤ w i\nhw' : ∑ i in s, w i = 1\nhz : ∀ (i : ι), i ∈ s → 0 ≤ z i\nhx : ∀ (i : ι), i ∈ s → w i ≠ 0 → z i = x\n⊢ ∏ i in s, z i ^ w i = ∑ i in s, w i * z i",
"tactic": "rw [geom_mean_weighte... | [
174,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | iteratedFDeriv_succ_apply_left | [] | [
1533,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1530,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.sub_imI | [] | [
273,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
9
] |
Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.BoundedFormula.relabel_not | [
{
"state_after": "no goals",
"state_before": "L : Language\nL' : Language\nM : Type w\nN : Type ?u.95799\nP : Type ?u.95802\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nγ : Type ?u.95830\nn : ℕ\ng : α → β ⊕ Fin n\nk : ℕ\nφ : BoundedFormula L α k\n⊢ relabe... | [
623,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ico_subset_Ioo_left | [
{
"state_after": "ι : Type ?u.22266\nα : Type u_1\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrder α\na a₁ a₂ b b₁ b₂ c x : α\nh : a₁ < a₂\n⊢ Set.Ico a₂ b ⊆ Set.Ioo a₁ b",
"state_before": "ι : Type ?u.22266\nα : Type u_1\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrder α\na a₁ a₂ b b₁ b₂ c x : α\nh : a₁ < a... | [
212,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.prod_self_le_prod_self | [] | [
1723,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1722,
1
] |
Mathlib/GroupTheory/FreeProduct.lean | FreeProduct.NeWord.append_head | [] | [
613,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
611,
1
] |
Std/Logic.lean | forall_comm | [] | [
491,
43
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
490,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.cokernelIsoOfEq_hom_comp_desc | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝⁴ : Category C\ninst✝³ : HasZeroMorphisms C\nX Y : C\nf✝ : X ⟶ Y\ninst✝² : HasCokernel f✝\nZ : C\nf g : X ⟶ Y\ninst✝¹ : HasCokernel f\ninst✝ : HasCokernel g\nh : f = g\ne : Y ⟶ Z\nhe : g ≫ e = 0\n⊢ f ≫ e = 0",
"tactic": "simp [h, he]"
},
... | [
842,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
839,
1
] |
Mathlib/Data/Finsupp/Lex.lean | Pi.lex_eq_finsupp_lex | [] | [
42,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coe_copy | [] | [
168,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Data/List/Sigma.lean | List.map_dlookup_eq_find | [
{
"state_after": "case pos\nα : Type u\nβ : α → Type v\nl✝ l₁ l₂ : List (Sigma β)\ninst✝ : DecidableEq α\na a' : α\nb' : β a'\nl : List (Sigma β)\nh : a = a'\n⊢ Option.map (Sigma.mk a) (dlookup a ({ fst := a', snd := b' } :: l)) =\n find? (fun s => decide (a = s.fst)) ({ fst := a', snd := b' } :: l)\n\ncase ... | [
231,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Algebra/Order/Module.lean | smul_neg_iff_of_pos | [
{
"state_after": "k : Type u_1\nM : Type u_2\nN : Type ?u.2442\ninst✝³ : OrderedSemiring k\ninst✝² : OrderedAddCommGroup M\ninst✝¹ : Module k M\ninst✝ : OrderedSMul k M\na b : M\nc : k\nhc : 0 < c\n⊢ 0 < c • -a ↔ 0 < -a",
"state_before": "k : Type u_1\nM : Type u_2\nN : Type ?u.2442\ninst✝³ : OrderedSemirin... | [
47,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/Data/List/Lattice.lean | List.forall_mem_of_forall_mem_union_right | [] | [
130,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Ring.lean | summable_mul_prod_iff_summable_mul_sigma_antidiagonal | [] | [
203,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.map_sup_comap_of_surjective | [] | [
642,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
640,
1
] |
Mathlib/Topology/MetricSpace/Equicontinuity.lean | Metric.uniformEquicontinuous_of_continuity_modulus | [
{
"state_after": "α : Type u_3\nβ : Type u_2\nι✝ : Type ?u.4017\ninst✝¹ : PseudoMetricSpace α\nι : Type u_1\ninst✝ : PseudoMetricSpace β\nb : ℝ → ℝ\nb_lim : Tendsto b (𝓝 0) (𝓝 0)\nF : ι → β → α\nH : ∀ (x y : β) (i : ι), dist (F i x) (F i y) ≤ b (dist x y)\n⊢ ∀ (ε : ℝ), ε > 0 → ∃ δ, δ > 0 ∧ ∀ (x y : β), dist x... | [
117,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/LinearAlgebra/Determinant.lean | LinearMap.det_eq_one_of_subsingleton | [
{
"state_after": "R : Type u_2\ninst✝¹⁰ : CommRing R\nM : Type u_1\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : Module R M\nM' : Type ?u.929764\ninst✝⁷ : AddCommGroup M'\ninst✝⁶ : Module R M'\nι : Type ?u.930306\ninst✝⁵ : DecidableEq ι\ninst✝⁴ : Fintype ι\ne : Basis ι R M\nA : Type ?u.930784\ninst✝³ : CommRing A\ninst✝² ... | [
296,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.comp_familyOfBFamily | [] | [
1238,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1236,
1
] |
Mathlib/Deprecated/Group.lean | MulEquiv.isMonoidHom | [] | [
160,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Algebra/Order/Interval.lean | NonemptyInterval.coe_one_interval | [] | [
75,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousMap.modulus_pos | [] | [
387,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Order/PartialSups.lean | partialSups_eq_sup'_range | [
{
"state_after": "case zero\nα : Type u_1\ninst✝ : SemilatticeSup α\nf : ℕ → α\n⊢ ↑(partialSups f) Nat.zero = Finset.sup' (Finset.range (Nat.zero + 1)) (_ : ∃ x, x ∈ Finset.range (Nat.zero + 1)) f\n\ncase succ\nα : Type u_1\ninst✝ : SemilatticeSup α\nf : ℕ → α\nn : ℕ\nih : ↑(partialSups f) n = Finset.sup' (Fins... | [
128,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
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